Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince

Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(G\) with increasing \(B\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.

Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:

model 1: simple model \(G = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 2: phi model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 3: phi-alpha model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)

sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

NOTE:

This document contains a temporally balanced set of \(G\) observations. First, the data set limited to plots that meet our plot-based filtering criteria (see below). Then the data set was further restricted to plots with at least 2 \(G\) observations (i.e., three FIA tree census records), with one in each of the two following decades: 2000-2010 (including censuses part of FIA 3.0 from 1996-2000 as part of the 2000 panel), and 2011-2022. For plots that had >2 \(G\) observations we took the first and last ones.

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

  • case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)

  • case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)

  • case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)

  • case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1677 observations.

Below the model fitting procedure is implemented by ecoprovince:

Temporally-balancing the biomass growth data set

Lets look at some quick attributes of the dataset:

  • The data set has 104986 observations, comprised of 55492 plots.
  • The frequency of growth measurements among plots is as follows : 25149, 13819, 13897, 2627.
  • Thus 54.68 % of plots have at least two growth intervals.

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   4772     3408.2                                
## 2   4771     3405.7  1   2.487   3.4837 0.06204 .  
## 3   4770     3236.8  1 168.924 248.9422 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 17319.61
## 2     2 17318.13
## 3     3 17077.21
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.139845   0.161516   0.866    0.387    
## phi   0.006338   0.004974   1.274    0.203    
## alpha 0.617108   0.036755  16.790   <2e-16 ***
## A     3.642778   0.116441  31.284   <2e-16 ***
## k     9.993586   0.836456  11.948   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8238 on 4770 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.089e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   4770     3236.8                              
## 2   4769     3230.7  1 6.0211  8.8879 0.002885 **
## 3   4769     3231.1  0 0.0000                    
## 4   4768     3230.6  1 0.5307  0.7832 0.376203   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 17077.21
## 2    3a 17070.32
## 3    3b 17070.93
## 4    3c 17072.14
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.144797   0.161620   0.896 0.370346    
## phi    0.005887   0.004966   1.185 0.235888    
## alpha  0.614851   0.036732  16.739  < 2e-16 ***
## A      3.724218   0.125492  29.677  < 2e-16 ***
## k     16.260444   3.008359   5.405 6.79e-08 ***
## p      0.197628   0.056420   3.503 0.000465 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8231 on 4769 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.737e-07
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9672, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -14.071, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1050 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  11685     9455.5                                
## 2  11682     9416.9  3  38.62   15.97 2.333e-10 ***
## 3  11681     8761.0  1 655.85  874.44 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 40222.79
## 2     2 40171.87
## 3     3 39330.25
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.554938   0.141202   3.930 8.54e-05 ***
## phi    0.026295   0.003682   7.142 9.72e-13 ***
## alpha  0.829228   0.025725  32.235  < 2e-16 ***
## A      2.959101   0.077541  38.162  < 2e-16 ***
## k     14.496808   0.635461  22.813  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.866 on 11681 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.138e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  11681     8761.0                                
## 2  11680     8663.0  1 97.989 132.115 < 2.2e-16 ***
## 3  11680     8686.7  0  0.000                      
## 4  11679     8662.8  1 23.906  32.229 1.403e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 39330.25
## 2    3a 39200.81
## 3    3b 39232.70
## 4    3c 39202.49
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.541180   0.139710   3.874 0.000108 ***
## phi    0.026504   0.003654   7.254 4.31e-13 ***
## alpha  0.819098   0.025587  32.013  < 2e-16 ***
## A      3.212284   0.092789  34.619  < 2e-16 ***
## k     30.206408   2.545767  11.865  < 2e-16 ***
## p      0.188297   0.013330  14.126  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8612 on 11680 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 4.164e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1031 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   5341     5688.8                               
## 2   5340     5688.7  1   0.072   0.0674 0.7952    
## 3   5339     5460.2  1 228.449 223.3761 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 22327.72
## 2     2 22329.65
## 3     3 22112.62
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -1.3566162  0.0943389 -14.380   <2e-16 ***
## phi   -0.0003043  0.0053930  -0.056    0.955    
## alpha  0.6601464  0.0417385  15.816   <2e-16 ***
## A      6.2586687  0.1870844  33.454   <2e-16 ***
## k     20.8894391  2.0689590  10.097   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.011 on 5339 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.62e-06
##   (6 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5339     5460.2                                
## 2   5338     5413.6  1 46.661   46.01 1.304e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 22112.62
## 2    3a 22068.76
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -1.383e+00  9.279e-02 -14.906  < 2e-16 ***
## phi    1.158e-04  5.368e-03   0.022    0.983    
## alpha  6.595e-01  4.125e-02  15.989  < 2e-16 ***
## A      7.706e+00  4.701e-01  16.392  < 2e-16 ***
## k      1.101e+02  2.780e+01   3.960 7.58e-05 ***
## p      3.385e-01  2.446e-02  13.837  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.007 on 5338 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 8.604e-06
##   (6 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).
## Warning: Removed 1036 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   3242     2626.1                                
## 2   3241     2621.0  1   5.045   6.2389 0.01255 *  
## 3   3240     2415.5  1 205.472 275.6030 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 11966.08
## 2     2 11961.84
## 3     3 11698.93
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.139424   0.216948  -0.643   0.5205    
## phi    0.023646   0.009365   2.525   0.0116 *  
## alpha  0.826107   0.045276  18.246   <2e-16 ***
## A      4.746405   0.209613  22.644   <2e-16 ***
## k     32.364828   2.388594  13.550   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8634 on 3240 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.622e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3240     2415.5                                
## 2   3239     2355.4  1 60.127  82.683 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 11698.93
## 2    3a 11619.13
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.172399   0.211318  -0.816   0.4147    
## phi     0.021007   0.009159   2.294   0.0219 *  
## alpha   0.818058   0.044729  18.289  < 2e-16 ***
## A       6.400734   0.440119  14.543  < 2e-16 ***
## k     117.199700  18.633196   6.290  3.6e-10 ***
## p       0.175050   0.012112  14.453  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8528 on 3239 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.67e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95574, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.702, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 1108 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value    Pr(>F)    
## 1   6041     5944.5                                 
## 2   6040     5937.2  1   7.30   7.4261  0.006447 ** 
## 3   6039     5759.7  1 177.55 186.1577 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 23796.36
## 2     2 23790.93
## 3     3 23609.43
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.282209   0.095635 -13.407   <2e-16 ***
## phi   -0.018755   0.006927  -2.707   0.0068 ** 
## alpha  0.629953   0.043517  14.476   <2e-16 ***
## A      6.705014   0.227860  29.426   <2e-16 ***
## k     47.968739   3.668489  13.076   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9766 on 6039 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.873e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     3 23609.43
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.282209   0.095635 -13.407   <2e-16 ***
## phi   -0.018755   0.006927  -2.707   0.0068 ** 
## alpha  0.629953   0.043517  14.476   <2e-16 ***
## A      6.705014   0.227860  29.426   <2e-16 ***
## k     47.968739   3.668489  13.076   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9766 on 6039 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.873e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 1145 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   7528      13282                              
## 2   7527      13280  1    1.3   0.7363 0.3909    
## 3   7526      11939  1 1341.4 845.5545 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 37078.46
## 2     2 37079.73
## 3     3 36279.86
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.349482   0.105426  -3.315 0.000921 ***
## phi   -0.009491   0.005218  -1.819 0.068961 .  
## alpha  0.856907   0.026946  31.800  < 2e-16 ***
## A      5.817495   0.138279  42.071  < 2e-16 ***
## k      3.472531   0.361833   9.597  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.26 on 7526 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.303e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7526      11939                                
## 2   7525      11887  1 52.526 33.2522 8.415e-09 ***
## 3   7525      11886  0  0.000                      
## 4   7524      11885  1  1.393  0.8819    0.3477    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 36279.86
## 2    3a 36248.65
## 3    3b 36248.43
## 4    3c 36249.54
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.379037   0.104055  -3.643 0.000272 ***
## phi   -0.009317   0.005197  -1.793 0.073059 .  
## alpha  0.854135   0.026807  31.862  < 2e-16 ***
## A      6.816954   0.438500  15.546  < 2e-16 ***
## k      3.410291   0.872216   3.910 9.31e-05 ***
## s      0.464466   0.078786   5.895 3.90e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.257 on 7525 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.449e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1017 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   7564      16078                              
## 2   7563      16077  1    1.0   0.4711 0.4925    
## 3   7562      14784  1 1293.7 661.7408 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 37504.72
## 2     2 37506.25
## 3     3 36873.46
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.290227   0.130592  -2.222   0.0263 *  
## phi   -0.012769   0.005708  -2.237   0.0253 *  
## alpha  0.847614   0.029809  28.435   <2e-16 ***
## A      5.613649   0.169380  33.142   <2e-16 ***
## k      9.756220   0.724398  13.468   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.398 on 7562 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.119e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7562      14784                                 
## 2   7561      14633  1 150.558  77.794 < 2.2e-16 ***
## 3   7561      14672  0   0.000                      
## 4   7560      14630  1  41.445  21.416 3.759e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 36873.46
## 2    3a 36798.00
## 3    3b 36818.10
## 4    3c 36798.69
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.299719   0.129141  -2.321   0.0203 *  
## phi   -0.013278   0.005661  -2.345   0.0190 *  
## alpha  0.839169   0.029556  28.392  < 2e-16 ***
## A      6.046706   0.206060  29.344  < 2e-16 ***
## k     27.065470   4.019008   6.734 1.77e-11 ***
## p      0.283510   0.025089  11.300  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.391 on 7561 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.725e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 981 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    780     1659.4                                 
## 2    779     1659.4  1   0.058  0.0273    0.8687    
## 3    778     1553.0  1 106.333 53.2677 7.195e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3854.426
## 2     2 3856.398
## 3     3 3806.544
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     0.3940896  0.8275950   0.476  0.63408    
## phi   -0.0009407  0.0260228  -0.036  0.97117    
## alpha  0.8166398  0.1004937   8.126 1.74e-15 ***
## A      4.4837908  0.7184812   6.241 7.15e-10 ***
## k     10.4572437  3.2639381   3.204  0.00141 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.413 on 778 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.01e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   parameters without starting value in 'data': p
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    778     1553.0                         
## 2    777     1549.6  1 3.4384  1.7241 0.1896
##   model      AIC
## 1     3 3806.544
## 2    3a 3806.808
## 3    3b 3807.724
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     0.3940896  0.8275950   0.476  0.63408    
## phi   -0.0009407  0.0260228  -0.036  0.97117    
## alpha  0.8166398  0.1004937   8.126 1.74e-15 ***
## A      4.4837908  0.7184812   6.241 7.15e-10 ***
## k     10.4572437  3.2639381   3.204  0.00141 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.413 on 778 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.01e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96129, p-value = 1.584e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.8967, p-value = 9.752e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1077 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1244     1027.5                                
## 2   1243     1025.3  1 2.2019  2.6694 0.1025447    
## 3   1242     1015.6  1 9.7198 11.8868 0.0005842 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4525.811
## 2     2 4525.136
## 3     3 4515.258
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.77575    0.28728  -2.700 0.007021 ** 
## phi    0.01703    0.01283   1.327 0.184685    
## alpha  0.38784    0.10800   3.591 0.000342 ***
## A      4.24498    0.31468  13.490  < 2e-16 ***
## k     23.59203    3.99166   5.910 4.41e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9043 on 1242 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.267e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1242    1015.58                                
## 2   1241     976.15  1 39.423  50.119 2.415e-12 ***
## 3   1240     974.33  1  1.821   2.317    0.1282    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 4515.258
## 2    3a 4467.887
## 3    3b       NA
## 4    3c 4467.559
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.84078    0.27177  -3.094 0.002021 ** 
## phi     0.01821    0.01256   1.449 0.147540    
## alpha   0.39633    0.10417   3.805 0.000149 ***
## A       5.45365    1.61675   3.373 0.000766 ***
## k     146.78996   71.07378   2.065 0.039100 *  
## s       2.15122    1.02725   2.094 0.036449 *  
## p       0.45332    0.15315   2.960 0.003136 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8864 on 1240 degrees of freedom
## 
## Number of iterations to convergence: 22 
## Achieved convergence tolerance: 8.354e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93154, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.4546, p-value = 1.085e-10
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1176 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1     39     89.982                         
## 2     38     89.834  1 0.1482  0.0627 0.8037
## 3     37     85.256  1 4.5777  1.9867 0.1670
##   model      AIC
## 1     1 193.9007
## 2     2 195.8314
## 3     3 195.6347
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)
## ge   4.5933    10.6637   0.431    0.669
## A    0.7165     0.9102   0.787    0.436
## k  -24.0560    14.7537  -1.631    0.111
## 
## Residual standard error: 1.519 on 39 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.243e-06
##   (368 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1     39     89.982                          
## 2     38     89.738  1 0.24349  0.1031 0.7499
##   model      AIC
## 1     1 193.9007
## 2    1a 195.7869
## 3    1b       NA
## 4    1c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)
## ge   4.5933    10.6637   0.431    0.669
## A    0.7165     0.9102   0.787    0.436
## k  -24.0560    14.7537  -1.631    0.111
## 
## Residual standard error: 1.519 on 39 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.243e-06
##   (368 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96947, p-value = 0.3169
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.2014, p-value = 0.2296
## alternative hypothesis: two.sided

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_263$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_263.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start,  : 
##   missing or negative weights not allowed
## Error in nls(fg_2, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   missing or negative weights not allowed
## Error in nls(fg_3, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   missing or negative weights not allowed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)  
## 1    127     112.40                            
## 2    126     112.13  1 0.26844  0.3016 0.5838  
## 3    125     109.08  1 3.04756  3.4922 0.0640 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 421.2904
## 2     2 422.9796
## 3     3 421.3975
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge   0.2726     1.7336   0.157   0.8753  
## A    4.1582     1.7879   2.326   0.0216 *
## k  101.1654    45.1400   2.241   0.0268 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9408 on 127 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.017e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    127      112.4                         
## 2    126      111.9  1 0.5007  0.5638 0.4541
##   model      AIC
## 1     1 421.2904
## 2    1a 422.7100
## 3    1b 423.2902
## 4    1c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge   0.2726     1.7336   0.157   0.8753  
## A    4.1582     1.7879   2.326   0.0216 *
## k  101.1654    45.1400   2.241   0.0268 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9408 on 127 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.017e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87973, p-value = 7.476e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.3275, p-value = 0.01994
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1140 row(s) containing missing values (geom_path).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(fg_1, data = G_342, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5065     3432.2                                 
## 2   5064     3422.9  1   9.366  13.857 0.0001994 ***
## 3   5063     3203.5  1 219.410 346.772 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18094.74
## 2     2 18082.89
## 3     3 17749.14
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.761618   0.197780   3.851 0.000119 ***
## phi   0.009659   0.004543   2.126 0.033552 *  
## alpha 0.637881   0.031901  19.996  < 2e-16 ***
## A     2.976393   0.110283  26.989  < 2e-16 ***
## k     3.772365   0.519549   7.261 4.43e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7954 on 5063 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.116e-06

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   5063     3203.5                              
## 2   5062     3198.9  1 4.5233  7.1577 0.007489 **
## 3   5062     3201.7  0 0.0000                    
## 4   5061     3196.5  1 5.1833  8.2067 0.004191 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 17749.14
## 2    3a 17743.98
## 3    3b 17748.33
## 4    3c 17742.12
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.764624   0.197840   3.865 0.000113 ***
## phi    0.009785   0.004551   2.150 0.031592 *  
## alpha  0.639624   0.031815  20.105  < 2e-16 ***
## A      2.920474   0.110104  26.525  < 2e-16 ***
## k     16.710125   3.563713   4.689 2.82e-06 ***
## p      0.550821   0.067920   8.110 6.31e-16 ***
## s      1.963671   0.527659   3.721 0.000200 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7947 on 5061 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 7.106e-06

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1108 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1   5101     7235.7                              
## 2   5100     7226.6  1   9.07   6.401 0.01144 *  
## 3   5099     7038.3  1 188.33 136.440 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 23011.44
## 2     2 23007.04
## 3     3 22874.26
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.717099   0.128899  -5.563 2.78e-08 ***
## phi   -0.014903   0.007147  -2.085   0.0371 *  
## alpha  0.731390   0.059496  12.293  < 2e-16 ***
## A      5.103329   0.170541  29.924  < 2e-16 ***
## k     11.127486   1.834527   6.066 1.41e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.175 on 5099 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.583e-06

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5099     7038.3                                
## 2   5098     6977.9  1 60.345  44.088 3.467e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 22874.26
## 2    3a 22832.31
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -7.976e-01  1.244e-01  -6.413 1.56e-10 ***
## phi   -1.168e-02  7.119e-03  -1.640    0.101    
## alpha  7.273e-01  5.855e-02  12.422  < 2e-16 ***
## A      1.970e+01  2.772e+01   0.711    0.477    
## k      1.969e+03  3.923e+03   0.502    0.616    
## p      1.847e-01  2.532e-01   0.729    0.466    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.17 on 5098 degrees of freedom
## 
## Number of iterations to convergence: 24 
## Achieved convergence tolerance: 8.167e-07

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 982 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    593     787.36                                
## 2    592     787.31  1  0.048  0.0361    0.8494    
## 3    591     765.62  1 21.688 16.7417 4.878e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2418.067
## 2     2 2420.030
## 3     3 2405.382
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     2.232485   1.433829   1.557   0.1200    
## phi   -0.008071   0.030152  -0.268   0.7890    
## alpha  0.855111   0.194706   4.392 1.33e-05 ***
## A      2.205356   0.463706   4.756 2.48e-06 ***
## k     16.759312   8.138542   2.059   0.0399 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.138 on 591 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 8.07e-06

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 2405.382
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     2.232485   1.433829   1.557   0.1200    
## phi   -0.008071   0.030152  -0.268   0.7890    
## alpha  0.855111   0.194706   4.392 1.33e-05 ***
## A      2.205356   0.463706   4.756 2.48e-06 ***
## k     16.759312   8.138542   2.059   0.0399 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.138 on 591 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 8.07e-06

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95527, p-value = 1.794e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.07064, p-value = 0.9437
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1175 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    663     866.92                                
## 2    662     854.80  1 12.120  9.3866  0.002275 ** 
## 3    661     829.09  1 25.702 20.4908 7.107e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2729.245
## 2     2 2721.868
## 3     3 2703.536
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.10198    1.56501   1.343  0.17970    
## phi    0.06479    0.02892   2.241  0.02539 *  
## alpha  0.80384    0.16677   4.820 1.78e-06 ***
## A      2.13854    0.49961   4.280 2.14e-05 ***
## k      9.61180    3.71444   2.588  0.00987 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.12 on 661 degrees of freedom
## 
## Number of iterations to convergence: 22 
## Achieved convergence tolerance: 9.664e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 2703.536
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.10198    1.56501   1.343  0.17970    
## phi    0.06479    0.02892   2.241  0.02539 *  
## alpha  0.80384    0.16677   4.820 1.78e-06 ***
## A      2.13854    0.49961   4.280 2.14e-05 ***
## k      9.61180    3.71444   2.588  0.00987 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.12 on 661 degrees of freedom
## 
## Number of iterations to convergence: 22 
## Achieved convergence tolerance: 9.664e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94157, p-value = 1.62e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.1287, p-value = 2.917e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1218 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    287     232.72                                 
## 2    286     231.62  1  1.0968  1.3543    0.2455    
## 3    285     212.75  1 18.8736 25.2837 8.764e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 815.8920
## 2     2 816.5219
## 3     3 793.8725
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.96003    1.22657  -0.783  0.43446    
## phi    0.04116    0.03686   1.117  0.26507    
## alpha  0.79777    0.13886   5.745 2.36e-08 ***
## A      3.07601    1.00185   3.070  0.00234 ** 
## k     37.38699   12.17334   3.071  0.00234 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.864 on 285 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.451e-06

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    285     212.75                          
## 2    284     212.69  1 0.05782  0.0772 0.7813
## 3    284     212.73  0 0.00000               
## 4    283     211.84  1 0.88809  1.1864 0.2770
##   model      AIC
## 1     3 793.8725
## 2    3a 795.7937
## 3    3b 795.8481
## 4    3c 796.6349
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.96003    1.22657  -0.783  0.43446    
## phi    0.04116    0.03686   1.117  0.26507    
## alpha  0.79777    0.13886   5.745 2.36e-08 ***
## A      3.07601    1.00185   3.070  0.00234 ** 
## k     37.38699   12.17334   3.071  0.00234 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.864 on 285 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.451e-06

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91999, p-value = 2.424e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.4932, p-value = 0.1354
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1264 row(s) containing missing values (geom_path).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3a
212 Laurentian Mixed Forest 3a
221 Eastern Broadleaf Forest 3a
222 Midwest Broadleaf Forest 3a
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3b
232 Outer Coastal Plain Mixed Forest 3a
234 Lower Mississippi Riverine Forest 3
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3c
255 Prairie Parkland (Subtropical) 1
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe 1
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3c
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3a
M223 Ozark Broadleaf Forest Meadow 3
M231 Ouachita Mixed Forest 3
M242 Cascade Mixed Forest NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.2.5 ge.97.5 phi phi.2.5 phi.97.5 alpha alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 4776 2388 0.1447972 -0.1720528 0.4616472 0.0058868 -0.0038484 0.0156220 0.6148505 0.5428383 0.6868628 3.724218 3.478196 3.970240 16.260444 10.3626711 22.158217
212 Laurentian Mixed Forest east 11688 5844 0.5411803 0.2673246 0.8150360 0.0265039 0.0193417 0.0336661 0.8190979 0.7689440 0.8692519 3.212284 3.030402 3.394166 30.206408 25.2162797 35.196537
221 Eastern Broadleaf Forest east 5350 2675 -1.3830516 -1.5649539 -1.2011492 0.0001158 -0.0104083 0.0106400 0.6594941 0.5786316 0.7403566 7.705926 6.784309 8.627543 110.104493 55.6037406 164.605245
222 Midwest Broadleaf Forest east 3248 1624 -0.1723992 -0.5867296 0.2419312 0.0210067 0.0030495 0.0389639 0.8180581 0.7303573 0.9057588 6.400734 5.537794 7.263673 117.199700 80.6656540 153.733746
223 Central Interior Broadleaf Forest east 6046 3023 -1.2822090 -1.4696880 -1.0947301 -0.0187547 -0.0323341 -0.0051753 0.6299529 0.5446443 0.7152614 6.705014 6.258327 7.151700 47.968739 40.7771918 55.160286
231 Southeastern Mixed Forest east 7532 3766 -0.3790368 -0.5830140 -0.1750597 -0.0093167 -0.0195043 0.0008708 0.8541345 0.8015847 0.9066843 6.816954 5.957372 7.676536 3.410291 1.7005048 5.120077
232 Outer Coastal Plain Mixed Forest east 7568 3784 -0.2997192 -0.5528716 -0.0465668 -0.0132776 -0.0243746 -0.0021806 0.8391689 0.7812309 0.8971070 6.046706 5.642770 6.450642 27.065470 19.1870985 34.943842
234 Lower Mississippi Riverine Forest east 784 392 0.3940896 -1.2304942 2.0186735 -0.0009407 -0.0520240 0.0501425 0.8166398 0.6193690 1.0139107 4.483791 3.073399 5.894182 10.457244 4.0500748 16.864413
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1248 624 -0.8407789 -1.3739527 -0.3076051 0.0182077 -0.0064416 0.0428570 0.3963256 0.1919630 0.6006881 5.453648 2.281780 8.625517 146.789957 7.3518120 286.228102
255 Prairie Parkland (Subtropical) pacific 410 205 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 104 52 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 132 66 0.2725824 -3.1578627 3.7030275 NA NA NA NA NA NA 4.158174 0.620298 7.696051 101.165354 11.8414505 190.489258
341 Intermountain Semi-Desert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 64 32 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5068 2534 0.7646237 0.3767708 1.1524767 0.0097851 0.0008633 0.0187070 0.6396243 0.5772539 0.7019947 2.920474 2.704623 3.136325 16.710125 9.7237058 23.696544
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5104 2552 -0.7976484 -1.0414924 -0.5538044 -0.0116772 -0.0256335 0.0022792 0.7272817 0.6125057 0.8420577 19.701104 -34.642618 74.044826 1968.521244 -5722.3479658 9659.390454
M223 Ozark Broadleaf Forest Meadow east 596 298 2.2324845 -0.5835366 5.0485056 -0.0080710 -0.0672890 0.0511471 0.8551105 0.4727115 1.2375095 2.205356 1.294643 3.116068 16.759312 0.7753286 32.743295
M231 Ouachita Mixed Forest east 668 334 2.1019804 -0.9710094 5.1749702 0.0647916 0.0080089 0.1215742 0.8038450 0.4763735 1.1313164 2.138543 1.157539 3.119547 9.611801 2.3182763 16.905326
M242 Cascade Mixed Forest pacific 6 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 290 145 -0.9600294 -3.3743152 1.4542563 0.0411591 -0.0313898 0.1137080 0.7977675 0.5244435 1.0710914 3.076007 1.104043 5.047971 37.386987 13.4259193 61.348056
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map2

## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 21 rows containing missing values (geom_point).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 22 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US  -0.2020562
## 2       pacific   0.0000000
## 3          east  -0.2011978
## 4 interior west  -0.4574107

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.003049736
## 2       pacific  0.000000000
## 3          east  0.002898228
## 4 interior west  0.022521022

alpha (biomass growth compensation effect)

##          region weighted.alpha
## 1     entire US      0.7358344
## 2       pacific      0.0000000
## 3          east      0.7436139
## 4 interior west      0.4365143

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   6.341731
## 2       pacific   0.000000
## 3          east   6.418035
## 4 interior west   2.718719

K (stand biomass at half biomss G in Mg/ha)

##          region weighted.k
## 1     entire US  202.43532
## 2       pacific    0.00000
## 3          east  205.23592
## 4 interior west   45.65293

Calculations - weighted averages subsetted to 15 ecoprovinces

  • ecoprovince codes: 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332

ge

##          region weighted.ge
## 1     entire US  -0.2030548
## 2       pacific   0.0000000
## 3          east  -0.2030836
## 4 interior west   0.0000000

phi

##          region weighted.phi
## 1     entire US  0.001858927
## 2       pacific  0.000000000
## 3          east  0.001859190
## 4 interior west  0.000000000

alpha

##          region weighted.alpha
## 1     entire US      0.7400673
## 2       pacific      0.0000000
## 3          east      0.7401722
## 4 interior west      0.0000000